Live (not decayed) radioisotopes on the Earth and Moon are messengers from recent nearby astrophysical explosions. Measurements of ⁶⁰Fe in deep-sea samples, Antarctic snow, and lunar regolith reveal two pulses about 3 Myr and 7 Myr ago. Detection of ²⁴⁴Pu in a deep-sea crust indicates a recent r-process event. We review the ultrasensitive accelerator mass spectrometry techniques that enable these findings. We then explore the implications for astrophysics, including supernova nucleosynthesis, particularly the r-process, as well as supernova dust production and the formation of the Local Bubble that envelops the Solar System. The implications go beyond nuclear physics and astrophysics to include studies of heliophysics, astrobiology, geology, and evolutionary biology.